Methods and apparatus for measuring a property of a substrate

ABSTRACT

In the measurement of properties of a wafer substrate, such as Critical Dimension or overlay a sampling plan is produced 2506 defined for measuring a property of a substrate, wherein the sampling plan comprises a plurality of sub-sampling plans. The sampling plan may be constrained to a predetermined fixed number of measurement points and is used 2508 to control an inspection apparatus to perform a plurality of measurements of the property of a plurality of substrates using different sub-sampling plans for respective substrates, optionally, the results are stacked 2510 to at least partially recompose the measurement results according to the sample plan.

This application incorporates by reference in their entireties U.S.patent application Ser. No. 14/355,962, filed May 2, 2014, InternationalApplication No. PCT/EP2012/073396 filed Nov. 22, 2012 and U.S.provisional application 61/579,969, filed Dec. 23, 2011.

FIELD

The present invention relates to methods of measuring a property of asubstrates, such as critical dimension or overlay, using a samplingplan, useable for example in the monitoring of the process of alithographic or other processing apparatus.

BACKGROUND

A lithographic apparatus is a machine that applies a desired patternonto a substrate, usually onto a target portion of the substrate. Alithographic apparatus can be used, for example, in the manufacture ofintegrated circuits (ICs). In that instance, a patterning device, whichis alternatively referred to as a mask or a reticle, may be used togenerate a circuit pattern to be formed on an individual layer of theIC. This pattern can be transferred onto a target portion (e.g.comprising part of, one, or several dies) on a substrate (e.g. a siliconwafer). Transfer of the pattern is typically via imaging onto a layer ofradiation-sensitive material (resist) provided on the substrate. Ingeneral, a single substrate will contain a network of adjacent targetportions that are successively patterned. Known lithographic apparatusinclude so-called steppers, in which each target portion is irradiatedby exposing an entire pattern onto the target portion at one time, andso-called scanners, in which each target portion is irradiated byscanning the pattern through a radiation beam in a given direction (the“scanning”-direction) while synchronously scanning the substrateparallel or anti parallel to this direction. It is also possible totransfer the pattern from the patterning device to the substrate byimprinting the pattern onto the substrate.

In order to monitor the lithographic process, parameters of thepatterned substrate are measured. Parameters may include, for example,the overlay error between successive layers formed in or on thepatterned substrate and critical linewidth of developed photosensitiveresist. This measurement may be performed on a product substrate and/oron a dedicated metrology target. There are various techniques for makingmeasurements of the microscopic structures formed in lithographicprocesses, including the use of scanning electron microscopes andvarious specialized tools. A fast and non-invasive form of specializedinspection tool is a scatterometer in which a beam of radiation isdirected onto a target on the surface of the substrate and properties ofthe scattered or reflected beam are measured. By comparing theproperties of the beam before and after it has been reflected orscattered by the substrate, the properties of the substrate can bedetermined. This can be done, for example, by comparing the reflectedbeam with data stored in a library of known measurements associated withknown substrate properties. Two main types of scatterometer are known.Spectroscopic scatterometers direct a broadband radiation beam onto thesubstrate and measure the spectrum (intensity as a function ofwavelength) of the radiation scattered into a particular narrow angularrange. Angularly resolved scatterometers use a monochromatic radiationbeam and measure the intensity of the scattered radiation as a functionof angle.

To support tighter lithography requirements, accurate correction of theperformance of the lithographic apparatus is required. In order to applymore accurate correction functionality, more data/dense sampling ofproducts on a substrate is required to determine a correction set. Usingthe trade-off between cost of metrology versus accuracy of a correctionset, it is common practice that a subset of all products is measured,with the intention to acquire approaching the same level of informationas is captured with fully measured products. This is called reducedsampling. Many mathematical approaches exist that support reducedsampling schemes, and these are typically based on geometricalconstraints (measurement sites per wafer location).

The effectiveness of a reduced sampling plan to achieve the bestaccuracy at the lowest possible metrology time/cost is currentlydetermined by a known applied mathematical approach. The appliedmathematical approach determines the limitation of the effectiveness ofa reduced sampling plan. This is discussed below with reference to FIG.8.

Current metrology sampling plans are static within a lot of exposedwafer substrates and all measured wafers are sampled with identicalsampling plans. Rarely, sampling plans are changed in between lots toadjust for changed state of the exposure and processing equipment.Usually, only a few wafers are measured within each lot to savemetrology time and cost.

For CPE (Corrections per Exposure), sometimes wafers are measured with avery dense sampling plan, usually very infrequently (for example onceevery few weeks).

Problems are:

1) Sampling only a few wafers of each lot may not yield results that arerepresentative for the lot. Wafers outside the regular population thatare measured will cause a disturbance in the APC (Advanced ProcessControl) feedback loop.

2) Wafers outside the regular population may escape detection if notmeasured.

3) CPE cannot be done very frequently because of the huge metrologycost.

SUMMARY

It is desirable to increase the effectiveness of a sampling plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a plurality of substrates, theinspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattered radiation        arising from the illumination; and    -   at least one processor configured to:    -   produce a sampling plan defined for measuring a property of a        substrate, wherein the sampling plan comprises a plurality of        sub-sampling plans; and    -   control the inspection apparatus to perform a plurality of        measurements of the property of a plurality of substrates using        different sub-sampling plans for respective substrates.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus according toany previous claim, the lithography apparatus comprising at least oneprocessor configured to:

-   -   control the exposure system to expose the plurality of        substrates prior to controlling the inspection apparatus to        perform the plurality of measurements of the property of the        plurality of substrates; and    -   control the exposure system to process a subsequent at least one        substrate with conditions based on the plurality of        measurements.

According to an aspect, there is provided a method of measuring aproperty of a substrate, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   updating the sampling plan separately in two or more        coordinates; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a method of measuring aproperty of a substrate, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   recording process setup information and processing the substrate        using a processing apparatus according to the process setup        information;    -   updating the sampling plan based on the process setup        information; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a method of measuring aproperty of a substrate, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   measuring processing data related to processing of the substrate        using a processing apparatus;    -   determining the variation of the processing data;    -   updating the sampling plan based on the variation of the        processing data; and    -   measuring the property of a substrate using the updated sampling        plan, wherein updating the sampling plan comprises modifying the        sampling across a substrate.

According to an aspect, there is provided a method of measuring aproperty of a substrate, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   measuring processing data related to processing of the substrate        using a processing apparatus;    -   measuring the property of a substrate;    -   determining the correlation of the measured processing data with        the measured property;    -   updating the sampling plan based on the correlation of the        processing data with the measured property; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a method of measuring aproperty of a substrate, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   measuring an angularly resolved spectrum of a substrate;    -   determining the variation of the angularly resolved spectrum;    -   updating the sampling plan based on the variation of the        angularly resolved spectrum; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a method of measuring aproperty of a plurality of substrates, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   decomposing the sampling plan into a plurality of sub-sampling        plans;    -   performing a plurality of measurements of the property of a        plurality of substrates using different sub-sampling plans on        respective substrates; and    -   stacking the results of the plurality of measurements to at        least partially recompose measurement results according to the        sampling plan.

According to an aspect, there is provided a method of measuring aproperty of a substrate, the method comprising the steps:

-   -   defining a sampling plan for measuring a property of a        substrate;    -   measuring the property of a substrate;    -   determining position-dependent variance of the measured        property;    -   updating the sampling plan based on the position-dependent        variance of the measured property; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   update the sampling plan separately in two or more coordinates;        and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded process setup information related to processing        of the substrate using a processing apparatus;    -   update the sampling plan based on the process setup information;        and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded processing data related to processing of the        substrate using a processing apparatus;    -   determine the variation of the processing data;    -   update the sampling plan based on the variation of the        processing data; and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan,

wherein the processor is configured to update the sampling plan bymodifying the sampling across a substrate.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded processing data related to processing of the        substrate using a processing apparatus;    -   control the inspection apparatus to measure the property of a        substrate;    -   determine the correlation of the measured processing data with        the measured property;    -   update the sampling plan based on the correlation of the        processing data with the measured property; and    -   measure the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   control the inspection apparatus to measure an angularly        resolved spectrum of a substrate;    -   determine the variation of the angularly resolved spectrum;    -   update the sampling plan based on the variation of the angularly        resolved spectrum; and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   decompose the sampling plan into a plurality of sub-sampling        plans;    -   control the inspection apparatus to perform a plurality of        measurements of the property of a plurality of substrates using        different sub-sampling plans on respective substrates; and    -   stack the results of the plurality of measurements to at least        partially recompose measurement results according to the        sampling plan.

According to an aspect, there is provided an inspection apparatusconfigured for measuring a property of a substrate, the inspectionapparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   control the inspection apparatus to measure the property of a        substrate;    -   determine position-dependent variance of the measured property;    -   update the sampling plan based on the position-dependent        variance of the measured property; and    -   measure the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   update the sampling plan separately in two or more coordinates;        and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   update the sampling plan separately in two or more coordinates;        and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded process setup information related to processing        of the substrate using a processing apparatus;    -   update the sampling plan based on the process setup information;        and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded process setup information related to processing        of the substrate using a processing apparatus;    -   update the sampling plan based on the process setup information;        and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded processing data related to processing of the        substrate using a processing apparatus;    -   determine the variation of the processing data;    -   update the sampling plan based on the variation of the        processing data; and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan,

wherein the processor is configured to update the sampling plan bymodifying the sampling across a substrate.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded processing data related to processing of the        substrate using a processing apparatus;    -   determine the variation of the processing data;    -   update the sampling plan based on the variation of the        processing data; and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan,

wherein the processor is configured to update the sampling plan bymodifying the sampling across a substrate.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded processing data related to processing of the        substrate using a processing apparatus;    -   control the inspection apparatus to measure the property of a        substrate;    -   determine the correlation of the measured processing data with        the measured property;    -   update the sampling plan based on the correlation of the        processing data with the measured property; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   receive recorded processing data related to processing of the        substrate using a processing apparatus;    -   control the inspection apparatus to measure the property of a        substrate;    -   determine the correlation of the measured processing data with        the measured property;    -   update the sampling plan based on the correlation of the        processing data with the measured property; and    -   measure the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   control the inspection apparatus to measure an angularly        resolved spectrum of a substrate;    -   determine the variation of the angularly resolved spectrum;    -   update the sampling plan based on the variation of the angularly        resolved spectrum; and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   control the inspection apparatus to measure an angularly        resolved spectrum of a substrate;    -   determine the variation of the angularly resolved spectrum;    -   update the sampling plan based on the variation of the angularly        resolved spectrum; and    -   control the inspection apparatus to measure the property of a        substrate using the updated sampling plan.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   decompose the sampling plan into a plurality of sub-sampling        plans;    -   control the inspection apparatus to perform a plurality of        measurements of the property of a plurality of substrates using        different sub-sampling plans on respective substrates; and    -   stack the results of the plurality of measurements to at least        partially recompose measurement results according to the        sampling plan.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   decompose the sampling plan into a plurality of sub-sampling        plans;    -   control the inspection apparatus to perform a plurality of        measurements of the property of a plurality of substrates using        different sub-sampling plans on respective substrates; and    -   stack the results of the plurality of measurements to at least        partially recompose measurement results according to the        sampling plan.

According to an aspect, there is provided a lithography apparatuscomprising an exposure system and an inspection apparatus, theinspection apparatus configured for measuring a property of a substrateand the inspection apparatus comprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   control the inspection apparatus to measure the property of a        substrate;    -   determine position-dependent variance of the measured property;    -   update the sampling plan based on the position-dependent        variance of the measured property; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a lithographic cellcomprising: a lithographic apparatus comprising an exposure system; andan inspection apparatus, the inspection apparatus configured formeasuring a property of a substrate and the inspection apparatuscomprising:

-   -   an illumination system configured to illuminate a substrate with        radiation;    -   a detection system configured to detect scattering properties        arising from the illumination; and    -   a processor configured to:    -   receive a sampling plan defined for measuring a property of a        substrate;    -   control the inspection apparatus to measure the property of a        substrate;    -   determine position-dependent variance of the measured property;    -   update the sampling plan based on the position-dependent        variance of the measured property; and    -   measuring the property of a substrate using the updated sampling        plan.

According to an aspect, there is provided a computer program productcontaining one or more sequences of machine-readable instructions formeasuring a property of a substrate, the instructions being adapted tocause one or more processors to perform a method or steps according toany of the aspects.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments will now be described, by way of example only, withreference to the accompanying schematic drawings in which correspondingreference symbols indicate corresponding parts, and in which:

FIG. 1 depicts a lithographic apparatus;

FIG. 2 depicts a lithographic cell or cluster including the apparatus ofFIG. 1;

FIG. 3 depicts a first scatterometer;

FIG. 4 depicts a second scatterometer;

FIG. 5 is a schematic diagram of control mechanisms in a lithographicprocess utilizing a scanner stability module;

FIG. 6 illustrates schematically the operation of the apparatus of FIG.1 in exposing a target portion (field) on a substrate;

FIG. 7 illustrates a level sensor apparatus in the lithography apparatusof FIG. 1;

FIG. 8 is a graph illustrating the effectiveness of reduced sampling;

FIG. 9 is a flowchart illustrating an embodiment with the sampling planupdated separately in two or more coordinates;

FIG. 10 is a flowchart illustrating an embodiment with the sampling planupdated based on process setup information;

FIG. 11 is a flowchart illustrating an embodiment with the sampling planupdated based on variation of measured scanner data;

FIG. 12 is a flowchart illustrating an embodiment with the sampling planupdated based on correlation of measured scanner data with the propertybeing measured according to the sample plan;

FIG. 13 is a flowchart illustrating an embodiment with the sampling planupdated based on variation of the angularly resolved spectrum of themetrology scatterometer;

FIG. 14 is a flowchart illustrating an embodiment with the sampling plandecomposed into a plurality of sub-sampling plans;

FIG. 15a illustrates a sampling plan for three wafers with completesampling of one wafer;

FIGS. 15b to 15c illustrate a sampling plan being decomposed acrosssub-sampling plans of three wafers;

FIGS. 16a and 16b illustrate a sampling plan being decomposed acrosssub-sampling plans of three wafers in a better way than illustrated inFIGS. 15b and 15 c;

FIG. 16c illustrates the exposure order for fields and a sub-samplingplan;

FIG. 17 illustrates a sampling plan being decomposed across sub-samplingplans of six wafers with some fields being not sampled;

FIG. 18 is a graph of correctable errors versus position across a wafer;

FIG. 19 is graph of correctable errors versus position across a wafer,with metrology noise added;

FIG. 20 is a flowchart illustrating an embodiment with the sampling planupdated based on position-dependent variation of the property beingmeasured;

FIG. 21 is a graph of four types of simulated noise versus positionacross a wafer;

FIG. 22 is a graph of calculated weighted model uncertainty for a noisetype with 10 nm wafer edge variance;

FIG. 23 is a graph of calculated weighted model uncertainty for a noisetype with 12 nm wafer edge variance;

FIG. 24 is a graph of calculated weighted model uncertainty for a noisetype with 10 nm wafer edge variance;

FIG. 25 is a flowchart illustrating an embodiment producing a samplingplan with sub-sampling plans that are used on respective wafers;

FIG. 26 is a flowchart illustrating an embodiment with a sampling planwith sub-sampling plans being produced based on variation of processingdata;

FIG. 27 is a flowchart illustrating an embodiment with a sampling planwith sub-sampling plans being produced based on correlation ofprocessing data with the property being measured;

FIG. 28 is a flowchart illustrating an embodiment with a sampling planwith sub-sampling plans being configured to be different in two or morecoordinates across a wafer; and

FIG. 29 is a flowchart illustrating an embodiment with a sampling planwith sub-sampling plans being updated separately in two or morecoordinates across a wafer.

DETAILED DESCRIPTION

FIG. 1 schematically depicts a lithographic apparatus. The apparatuscomprises:

-   -   an illumination system (illuminator) IL configured to condition        a radiation beam B (e.g. UV radiation or Extreme UV (EUV)        radiation).    -   a support structure (e.g. a mask table) MT constructed to        support a patterning device (e.g. a mask) MA and connected to a        first positioner PM configured to accurately position the        patterning device in accordance with certain parameters;    -   a substrate table (e.g. a wafer table) WT constructed to hold a        substrate (e.g. a resist-coated wafer) W and connected to a        second positioner PW configured to accurately position the        substrate in accordance with certain parameters; and    -   a projection system (e.g. a refractive projection lens system)        PS configured to project a pattern imparted to the radiation        beam B by patterning device MA onto a target portion C (e.g.        comprising one or more dies) of the substrate W.

The illumination system may include various types of optical components,such as refractive, reflective, magnetic, electromagnetic, electrostaticor other types of optical components, or any combination thereof, fordirecting, shaping, or controlling radiation.

The support structure supports, i.e. bears the weight of, the patterningdevice. It holds the patterning device in a manner that depends on theorientation of the patterning device, the design of the lithographicapparatus, and other conditions, such as for example whether or not thepatterning device is held in a vacuum environment. The support structurecan use mechanical, vacuum, electrostatic or other clamping techniquesto hold the patterning device. The support structure may be a frame or atable, for example, which may be fixed or movable as required. Thesupport structure may ensure that the patterning device is at a desiredposition, for example with respect to the projection system. Any use ofthe terms “reticle” or “mask” herein may be considered synonymous withthe more general term “patterning device.”

The term “patterning device” used herein should be broadly interpretedas referring to any device that can be used to impart a radiation beamwith a pattern in its cross-section such as to create a pattern in atarget portion of the substrate. It should be noted that the patternimparted to the radiation beam may not exactly correspond to the desiredpattern in the target portion of the substrate, for example if thepattern includes phase-shifting features or so called assist features.Generally, the pattern imparted to the radiation beam will correspond toa particular functional layer in a device being created in the targetportion, such as an integrated circuit.

The patterning device may be transmissive or reflective. Examples ofpatterning devices include masks, programmable mirror arrays, andprogrammable LCD panels. Masks are well known in lithography, andinclude mask types such as binary, alternating phase-shift, andattenuated phase-shift, as well as various hybrid mask types. An exampleof a programmable mirror array employs a matrix arrangement of smallmirrors, each of which can be individually tilted so as to reflect anincoming radiation beam in different directions. The tilted mirrorsimpart a pattern in a radiation beam which is reflected by the mirrormatrix.

The term “projection system” used herein should be broadly interpretedas encompassing any type of projection system, including refractive,reflective, catadioptric, magnetic, electromagnetic and electrostaticoptical systems, or any combination thereof, as appropriate for theexposure radiation being used, or for other factors such as the use ofan immersion liquid or the use of a vacuum. Any use of the term“projection lens” herein may be considered as synonymous with the moregeneral term “projection system”.

As here depicted, the apparatus is of a transmissive type (e.g.employing a transmissive mask). Alternatively, the apparatus may be of areflective type (e.g. employing a programmable mirror array of a type asreferred to above, or employing a reflective mask).

The lithographic apparatus may be of a type having two (dual stage) ormore substrate tables (and/or two or more mask tables). In such“multiple stage” machines the additional tables may be used in parallel,or preparatory steps may be carried out on one or more tables while oneor more other tables are being used for exposure.

The lithographic apparatus may also be of a type wherein at least aportion of the substrate may be covered by a liquid having a relativelyhigh refractive index, e.g. water, so as to fill a space between theprojection system and the substrate. An immersion liquid may also beapplied to other spaces in the lithographic apparatus, for example,between the mask and the projection system. Immersion techniques arewell known in the art for increasing the numerical aperture ofprojection systems. The term “immersion” as used herein does not meanthat a structure, such as a substrate, must be submerged in liquid, butrather only means that liquid is located between the projection systemand the substrate during exposure.

Referring to FIG. 1, the illuminator IL receives a radiation beam from aradiation source SO. The source and the lithographic apparatus may beseparate entities, for example when the source is an excimer laser. Insuch cases, the source is not considered to form part of thelithographic apparatus and the radiation beam is passed from the sourceSO to the illuminator IL with the aid of a beam delivery system BDcomprising, for example, suitable directing mirrors and/or a beamexpander. In other cases the source may be an integral part of thelithographic apparatus, for example when the source is a mercury lamp.The source SO and the illuminator IL, together with the beam deliverysystem BD if required, may be referred to as a radiation system.

The illuminator IL may comprise an adjuster AD for adjusting the angularintensity distribution of the radiation beam. Generally, at least theouter and/or inner radial extent (commonly referred to as σ-outer andσ-inner, respectively) of the intensity distribution in a pupil plane ofthe illuminator can be adjusted. In addition, the illuminator IL maycomprise various other components, such as an integrator IN and acondenser CO. The illuminator may be used to condition the radiationbeam, to have a desired uniformity and intensity distribution in itscross-section.

The radiation beam B is incident on the patterning device (e.g., maskMA), which is held on the support structure (e.g., mask table MT), andis patterned by the patterning device. Having traversed the mask MA, theradiation beam B passes through the projection system PS, which focusesthe beam onto a target portion C of the substrate W. With the aid of thesecond positioner PW and position sensor IF (e.g. an interferometricdevice, linear encoder or capacitive sensor), the substrate table WT canbe moved accurately, e.g. so as to position different target portions Cin the path of the radiation beam B. Similarly, the first positioner PMand another position sensor (which is not explicitly depicted in FIG. 1)can be used to accurately position the mask MA with respect to the pathof the radiation beam B, e.g. after mechanical retrieval from a masklibrary, or during a scan. In general, movement of the mask table MT maybe realized with the aid of a long-stroke module (coarse positioning)and a short-stroke module (fine positioning), which form part of thefirst positioner PM. Similarly, movement of the substrate table WT maybe realized using a long-stroke module and a short-stroke module, whichform part of the second positioner PW. In the case of a stepper (asopposed to a scanner) the mask table MT may be connected to ashort-stroke actuator only, or may be fixed. Mask MA and substrate W maybe aligned using mask alignment marks M1, M2 and substrate alignmentmarks P1, P2. Although the substrate alignment marks as illustratedoccupy dedicated target portions, they may be located in spaces betweentarget portions (these are known as scribe-lane alignment marks).Similarly, in situations in which more than one die is provided on themask MA, the mask alignment marks may be located between the dies.

The depicted apparatus could be used in at least one of the followingmodes:

1. In step mode, the mask table MT and the substrate table WT are keptessentially stationary, while an entire pattern imparted to theradiation beam is projected onto a target portion C at one time (i.e. asingle static exposure). The substrate table WT is then shifted in the Xand/or Y direction so that a different target portion C can be exposed.In step mode, the maximum size of the exposure field limits the size ofthe target portion C imaged in a single static exposure.

2. In scan mode, the mask table MT and the substrate table WT arescanned synchronously while a pattern imparted to the radiation beam isprojected onto a target portion C (i.e. a single dynamic exposure). Thevelocity and direction of the substrate table WT relative to the masktable MT may be determined by the (de-)magnification and image reversalcharacteristics of the projection system PS. In scan mode, the maximumsize of the exposure field limits the width (in the non-scanningdirection) of the target portion in a single dynamic exposure, whereasthe length of the scanning motion determines the height (in the scanningdirection) of the target portion.

3. In another mode, the mask table MT is kept essentially stationaryholding a programmable patterning device, and the substrate table WT ismoved or scanned while a pattern imparted to the radiation beam isprojected onto a target portion C. In this mode, generally a pulsedradiation source is employed and the programmable patterning device isupdated as required after each movement of the substrate table WT or inbetween successive radiation pulses during a scan. This mode ofoperation can be readily applied to maskless lithography that utilizesprogrammable patterning device, such as a programmable mirror array of atype as referred to above.

Combinations and/or variations on the above described modes of use orentirely different modes of use may also be employed.

FIG. 2 depicts a lithographic cell or cluster including the apparatus ofFIG. 1. As shown in FIG. 2, the lithographic apparatus LA forms part ofa lithographic cell LC, also sometimes referred to a ‘lithocell’ orcluster, which also includes apparatus to perform pre- and post-exposureprocesses on a substrate. Conventionally these include spin coaters SCto deposit resist layers, developers DE to develop exposed resist, chillplates CH and bake plates BK. A substrate handler, or robot, RO picks upsubstrates from input/output ports I/O1, I/O2, moves them between thedifferent process apparatus and delivers then to the loading bay LB ofthe lithographic apparatus. These devices, which are often collectivelyreferred to as the track, are under the control of a track control unitTCU which is itself controlled by the supervisory control system SCS,which also controls the lithographic apparatus via lithography controlunit LACU. Thus, the different apparatus can be operated to maximizethroughput and processing efficiency.

In order that the substrates that are exposed by the lithographicapparatus are exposed correctly and consistently, it is desirable toinspect exposed substrates to measure properties such as linethicknesses, critical dimensions (CD), etc. If errors are detected,adjustments may be made to exposures of subsequent substrates,especially if the inspection can be done soon and fast enough that othersubstrates of the same batch are still to be exposed. Also, alreadyexposed substrates may be stripped and reworked—to improve yield—ordiscarded, thereby avoiding performing exposures on substrates that areknown to be faulty. In a case where only some target portions of asubstrate are faulty, further exposures can be performed only on thosetarget portions which are good.

An inspection apparatus or metrology tool is used to determine theproperties of the substrates, and in particular, how the properties ofdifferent substrates or different layers of the same substrate vary fromlayer to layer. The inspection apparatus may be integrated into thelithographic apparatus LA or the lithocell LC or may be a stand-alonedevice. To enable most rapid measurements, it is desirable that theinspection apparatus measure properties in the exposed resist layerimmediately after the exposure. However, the latent image in the resisthas a very low contrast—there is only a very small difference inrefractive index between the parts of the resist which have been exposedto radiation and those which have not—and not all inspection apparatushave sufficient sensitivity to make useful measurements of the latentimage. Therefore measurements may be taken after the post-exposure bakestep (PEB) which is customarily the first step carried out on exposedsubstrates and increases the contrast between exposed and unexposedparts of the resist. At this stage, the image in the resist may bereferred to as semi-latent. It is also possible to make measurements ofthe developed resist image—at which point either the exposed orunexposed parts of the resist have been removed—or after a patterntransfer step such as etching. The latter possibility limits thepossibilities for rework of faulty substrates but may still provideuseful information.

FIG. 3 depicts a scatterometer. It comprises a broadband (white light)radiation projector 2 which projects radiation onto a substrate W. Thereflected radiation is passed to a spectrometer detector 4, whichmeasures a spectrum 10 (intensity as a function of wavelength) of thespecular reflected radiation. From this data, the structure or profilegiving rise to the detected spectrum may be reconstructed by processingunit PU, e.g. by Rigorous Coupled Wave Analysis and non-linearregression or by comparison with a library of simulated spectra as shownat the bottom of FIG. 3. In general, for the reconstruction the generalform of the structure is known and some parameters are assumed fromknowledge of the process by which the structure was made, leaving only afew parameters of the structure to be determined from the scatterometrydata. Such a scatterometer may be configured as a normal-incidencescatterometer or an oblique-incidence scatterometer.

Another scatterometer is shown in FIG. 4. In this device, the radiationemitted by radiation source 2 is collimated using lens system 12 andtransmitted through interference filter 13 and polarizer 17, reflectedby partially reflected surface 16 and is focused onto substrate W via amicroscope objective lens 15, which has a high numerical aperture (NA),preferably at least 0.9 and more preferably at least 0.95. Immersionscatterometers may even have lenses with numerical apertures over 1. Thereflected radiation then transmits through partially reflecting surface16 into a detector 18 in order to have the scatter spectrum detected.The detector may be located in the back-projected pupil plane 11, whichis at the focal length of the lens system 15, however the pupil planemay instead be re-imaged with auxiliary optics (not shown) onto thedetector. The pupil plane is the plane in which the radial position ofradiation defines the angle of incidence and the angular positiondefines azimuth angle of the radiation. The detector is preferably atwo-dimensional detector so that a two-dimensional angular scatterspectrum of a substrate target 30 can be measured. The detector 18 maybe, for example, an array of CCD or CMOS sensors, and may use anintegration time of, for example, 40 milliseconds per frame.

A reference beam is often used for example to measure the intensity ofthe incident radiation. To do this, when the radiation beam is incidenton the beam splitter 16 part of it is transmitted through the beamsplitter as a reference beam towards a reference mirror 14. Thereference beam is then projected onto a different part of the samedetector 18 or alternatively on to a different detector (not shown).

A set of interference filters 13 is available to select a wavelength ofinterest in the range of, say, 405-790 nm or even lower, such as 200-300nm. The interference filter may be tunable rather than comprising a setof different filters. A grating could be used instead of interferencefilters.

The detector 18 may measure the intensity of scattered light at a singlewavelength (or narrow wavelength range), the intensity separately atmultiple wavelengths or integrated over a wavelength range. Furthermore,the detector may separately measure the intensity of transversemagnetic- and transverse electric-polarized light and/or the phasedifference between the transverse magnetic- and transverseelectric-polarized light.

Using a broadband light source (i.e. one with a wide range of lightfrequencies or wavelengths—and therefore of colors) is possible, whichgives a large etendue, allowing the mixing of multiple wavelengths. Theplurality of wavelengths in the broadband preferably each has abandwidth of Δλ, and a spacing of at least 2 Δλ, (i.e. twice thebandwidth). Several “sources” of radiation can be different portions ofan extended radiation source which have been split using fiber bundles.In this way, angle resolved scatter spectra can be measured at multiplewavelengths in parallel. A 3-D spectrum (wavelength and two differentangles) can be measured, which contains more information than a 2-Dspectrum. This allows more information to be measured which increasesmetrology process robustness. This is described in more detail inEP1,628,164A.

The target 30 on substrate W may be a 1-D grating, which is printed suchthat after development, the bars are formed of solid resist lines. Thetarget 30 may be a 2-D grating, which is printed such that afterdevelopment, the grating is formed of solid resist pillars or vias inthe resist. The bars, pillars or vias may alternatively be etched intothe substrate. This pattern is sensitive to chromatic aberrations in thelithographic projection apparatus, particularly the projection systemPL, and illumination symmetry and the presence of such aberrations willmanifest themselves in a variation in the printed grating. Accordingly,the scatterometry data of the printed gratings is used to reconstructthe gratings. The parameters of the 1-D grating, such as line widths andshapes, or parameters of the 2-D grating, such as pillar or via widthsor lengths or shapes, may be input to the reconstruction process,performed by processing unit PU, from knowledge of the printing stepand/or other scatterometry processes.

A key component of accurate lithography is an ability to calibrateindividual lithographic apparatus. In addition to general parametersaffecting the whole substrate area, it is known to map and model theerror ‘fingerprint’ of an individual apparatus across the substratearea. This fingerprint, which can be established in terms of focus, doseand/or alignment, can be used during exposure to correct theidiosyncrasies of that apparatus, and thereby achieve a more accuratepatterning.

Improvements to the apparatus's focus and overlay (layer-to-layeralignment) uniformity have recently been achieved by the applicant'sBaseliner™ scanner stability module, leading to an optimized processwindow for a given feature size and chip application, enabling thecontinuation the creation of smaller, more advanced chips. The scannerstability module may automatically reset the system to a pre-definedbaseline each day. To do this it retrieves standard measurements takenfrom a monitor wafer using a metrology tool. The monitor wafer isexposed using a special reticle containing special scatterometry marks.From that day's measurements, the scanner stability module determineshow far the system has drifted from its baseline. It then calculateswafer-level overlay and focus correction sets. The lithography systemthen converts these correction sets into specific corrections for eachexposure on subsequent production wafers.

FIG. 5 depicts the overall lithography and metrology methodincorporating the scanner stability module 500 (essentially anapplication running on a server, in this example). Shown are three mainprocess control loops. The first loop provides the local scanner controlusing the scanner stability module 500 and monitor wafers. The monitorwafer 505 is shown being passed from the main lithography unit 510,having been exposed to set the baseline parameters for focus andoverlay. At a later time, metrology tool 515 reads these baselineparameters, which are then interpreted by the scanner stability module500 so as to calculate correction routines so as to provide scannerfeedback 550, which is passed to the main lithography unit 510, and usedwhen performing further exposures.

The second Advanced Process Control (APC) loop is for local scannercontrol on-product (determining focus, dose, and overlay). The exposedproduct wafer 520 is passed to metrology tool 515 where informationrelating to the critical dimensions, sidewall angles and overlay isdetermined and passed onto the Advanced Process Control (APC) module525. This data is also passed to the scanner stability module 500.Process corrections 540 are made before the Manufacturing ExecutionSystem (MES) 535 takes over, providing scanner control to the mainlithography unit 510, in communication with the scanner stability module500.

The third loop is to allow metrology integration into the second APCloop (e.g. for double patterning). The post etched wafer 530 is passedto metrology tool 515 which again passes information relating to thecritical dimensions, sidewall angles and overlay, read from the wafer,to the Advanced Process Control (APC) module. The loop continues thesame as with the second loop.

FIG. 6 illustrates schematically the scanning operation to expose onefield F on a substrate W in the lithographic apparatus of FIG. 1. Thesubstrate W and mask MA are seen in perspective view, with theillumination source IL above and the projection system PS in between.Mask MA carries a transparent pattern F′ which is a scaled up version ofthe pattern to be applied to one field F on substrate W. Illuminationsource IL presents a slit of radiation S′, not large enough in the Ydirection to cover the area F′ but wide enough in the X direction. Toexpose the entire field, the mask MA is moved through the area of slitS′ to project a corresponding slit area S on substrate field F. Thesemovements are represented by large arrows.

Conceptually, it is sufficient to regard the substrate as staying still,while the patterned slit S passes over it in the opposite sense of the Ydirection, as shown by the schematic plan detail to the right of thediagram. The slit with length L is moved with an exposure velocity Vexpover field F.

Parameters of the projection system PS and control set points areadjusted prior to exposure to ensure that distortion within the slit isconstant over the whole exposure. Certain parameters, for example focusset points, may be controlled dynamically throughout the scanningmovement, to maintain optimum, uniform patterning quality across thefield.

FIG. 7 is a perspective view of level mapping operations taking place ina lithographic apparatus. Substrate table WT is shown with a substrate Wloaded thereon which is being measured by a level sensor comprising alevel sensing projector LSP and a level sensing detector LSD. Analignment sensor AS is provided for measuring X-Y position across thesubstrate. Position sensor IF, seen in FIG. 1, is seen in more detail inFIG. 4. A pair of Z-direction position sensors IF(Z) are provided (inthis example, interferometers), while IF(X) represents rays of theX-direction interferometer, and IF(Y) represents rays of the Y-directioninterferometer. Other forms of position sensor may be used, for example,encoder plates, as is known to the skilled person.

In operation of the level sensor, a number of level sensing “spots” areprojected onto a line-shaped portion of the substrate surface, byprojector LSP, and reflected from the substrate surface to be imaged inthe level sensing detector LSD.

FIG. 8 is a graph illustrating the effectiveness of reduced sampling.

The vertical axis, P, is the performance metric after correction, forexample overlay residuals. The horizontal axis, N, is the number ofmeasurement points in the sampling plan used for determination of thecorrections. Better performance is a lower value of P, which istypically achieved by increasing the number of sample points N. NF isthe number of measurement points at which the wafer is fully measured,which gives the best performance, at the cost of time consumingsampling. The curve 802 is the optimal curve based on geometricconstraints.

Embodiments described herein improve the effectiveness of reducedsampling to provide an improved curve 804, such that faster measurements(with fewer measurement points) are achievable 806 for the sameperformance, or better performance is achieved 808 for the samemeasurement time.

FIG. 9 is a flowchart illustrating an embodiment with the sampling planupdated separately in two or more coordinates. In this embodiment, theapproach is to update sampling schemes separately for x, y and/or r(radius) within one process layer. The particular scheme is determinedby application (for example, it can be x or y only, orsummation/highest/lowest x or y per area, or per radius). Implementationcan be via segmented metrology targets, which are dedicated either to xor y. The motivations of this approach include:

1) scanner and/or metrology equipment have different budgets for x andy, therefore the noise contribution in x, y will be different leading toa delta in required sampling for similar model uncertainty;

2) in the case of double exposure (split in x, y, also known as griddeddesign), with reference to different layers the overlay requirements forx, y are different, therefore the required model uncertainty will bedifferent; and

3) different process influences in x, y, for instance CMP (ChemicalMechanical Polishing/Planarization) or annealing steps produce localradial fingerprints where the model uncertainty is quite different in xversus y. This can, but does not have to be, expressed by a radialfunction as well.

The steps in this embodiment include:

902—defining a sampling plan for measuring a property of a wafer.

904—recording process setup information and processing the wafer usingthe scanner tool according to the process setup information. The processsetup information may include parameters of the projection system PSillustrated in FIG. 6 and exposure and focus control set points. Theprocess setup information may relate to other processing apparatusrather than scanners, for example other lithographic apparatus oretching apparatus. Thus the embodiments described herein are not limitedto lithography apparatus.

906—updating the sampling plan separately in two or more coordinates. Ifstep 904 is performed, this updating of the sampling plan is based onthe recorded process setup information. The updating of the samplingplan may include modifying the sampling across a wafer, for example bychanging the sampling density and/or locations within the wafer, basedfor example upon the recorded process setup information.

908—measuring the property of a wafer using the updated sampling plan.

Alternatively to using step 904 and in step 906 updating the samplingplan based on process setup information, the method may include steps asdescribed with reference to FIG. 11:

-   -   measuring processing data related to processing of the wafer        using a scanner; and    -   determining the variation of the processing data,

and the updating of the sampling plan in step 906 is based on thevariation of the processing data.

Alternatively to using step 904 and in step 906 updating the samplingplan based on process setup information, the method may include steps asdescribed with reference to FIG. 12:

-   -   measuring processing data related to processing of the wafer        using a scanner;    -   measuring the property of a substrate; and    -   determining the correlation of the processing data with the        property,

and the updating of the sampling plan in step 906 is based on thecorrelation of the processing data with the property.

FIG. 10 is a flowchart illustrating an embodiment with the sampling planupdated based on process setup information. In this embodiment,determination of a sampling plan may make use of constraints based onscanner (process job) information (for example scan direction, whichchuck is used in a twin wafer chuck lithography apparatus, wafer layout)or actuator information (for example number of fingers that can beactuated to define the illumination dose in a scanner). The processsetup information may thus include parameters of the projection systemPS illustrated in FIG. 6 and exposure and focus control set points.

The steps in this embodiment include:

1002—defining a sampling plan for measuring a property of a wafer.

1004—recording process setup information and processing the wafer usingthe scanner tool according to the process setup information. The processsetup information may for example comprise scanner process jobinformation or scanner actuator information. The process setupinformation may relate to other processing apparatus (tools) rather thanscanners, for example other lithographic apparatus or etching apparatus.

1006—updating the sampling plan based on the process setup information.The updating of the sampling plan may include modifying the samplingacross a wafer, for example by changing the sampling density and/orlocations within the wafer, based for example upon the recorded processsetup information.

1008—measuring the property of a wafer using the updated sampling plan.

FIG. 11 is a flowchart illustrating an embodiment with the sampling planupdated based on variation of measured scanner data. In this embodiment,the approach is determination of a sampling plan by analyzing alignmentdata/leveling data of a similar or the same wafer, where homogeneity oruncertainty per area/wafer can be classified. For example an area with alarge variation in MCC (multiple correlation coefficient)/WQ (waferquality) or topology requires denser sampling. The approach of anembodiment is to monitor fingerprints of alignment data/leveling dataand increase sampling on locations where fingerprint changes aredetected.

The steps include:

1102—defining a sampling plan for measuring a property of a wafer.

1104—processing a wafer using the scanner.

1106—measuring processing data related to processing of the wafer usinga scanner. The processing data may for example comprise alignment dataand/or leveling data.

1108—determining the variation of the processing data.

1110—updating the sampling plan based on the variation of the processingdata. Updating the sampling plan includes modifying the sampling acrossa wafer, for example by changing the sampling density and/or locationswithin the wafer, based for example upon the variation of the processingdata.

1112—measuring the property of a wafer using the updated sampling plan.

FIG. 12 is a flowchart illustrating an embodiment with the sampling planupdated based on correlation of measured scanner data with the propertybeing measured according to the sample plan. In this embodiment, theapproach is determination of a sampling plan using a known correlationbetween alignment data/leveling data and overlay/CDU (CD uniformity)data and to identify areas or wafers with better or worse correlation.Higher correlation would require less sampling.

The steps in this embodiment include:

1202—defining a sampling plan for measuring a property of a wafer.

1204—processing a wafer using the scanner.

1206—measuring processing data related to processing of the wafer usinga scanner. The processing data may comprise alignment data and/orleveling data.

1208—measuring the property of a substrate; and

1210—determining the correlation of the processing data with theproperty

1212—updating the sampling plan based on the correlation of theprocessing data with the property. The updating of the sampling plan mayinclude modifying the sampling across a wafer, for example by changingthe sampling density and/or locations within the wafer, based forexample upon the variation of the processing data.

1214—measuring the property of a wafer using the updated sampling plan.

FIG. 13 is a flowchart illustrating an embodiment with the sampling planupdated based on variation of the angularly resolved spectrum of themetrology scatterometer. The variation is a measure of the smoothness ofthe angular spectrum across the pupil plane of the scatterometer and thevariation is sensitive to processing effects.

The steps are:

1302—defining a sampling plan for measuring a property of a wafer.

1304—processing a wafer using the scanner.

1306—measuring an angularly resolved spectrum of the wafer.

1308—determining the variation (for example standard deviation, sigma)of the angularly resolved spectrum. The variation may be estimated froma single measurement point.

1310—updating the sampling plan based on the variation of the angularlyresolved spectrum. and

1312—measuring the property of a wafer using the updated sampling plan.

FIG. 14 is a flowchart illustrating an embodiment with the sampling plandecomposed into a plurality of sub-sampling plans. By decomposing adense sampling scheme and distributing over all the wafers in a lot, ormultiple lots, processing drifts can be averaged, making themeasurements more representative of the complete lot. Each wafer may bemeasured, enabling early flagging of wafers that suffer from largeexcursions. These wafers can be excluded from APC feedback loop updatesand can be reworked instead of processed further. CPE corrections can bedetermined for each lot, allowing a faster and better feedback for CPE.

With reference to FIG. 14, the steps are:

1402—defining a sampling plan for measuring a property of a wafer.

1404—decompose the sampling plan into a plurality of sub-sampling plans.The sampling plan may be decomposed into a plurality of sub-samplingplans across a plurality of exposure fields of the wafers.

1406—performing a plurality of measurements of the property of aplurality of wafers using different sub-sampling plans on respectivewafers.

1408—stacking the results of the plurality of measurements to at leastpartially recompose the measurement results according to the sampleplan.

FIG. 15a illustrates a sampling plan for three wafers with completesampling of one wafer. With reference to FIG. 15a , a production lot hasthree wafers 1502-1506, of which only the second wafer 1504 is sampled.The squares 1508 are exposure fields, the dots 1510 are sample points inthe sample plan and the large circles 1502-1504 represent the wafers.The approach of distributed sampling in accordance with an embodiment isto include the first and last wafers 1502 and 1506 (all wafers in thiscase) in the sampling plan, without increasing the total number ofsampling points (12×9 in this example) per lot. That can be achieved inseveral ways, for instance using only the four center fields on allwafers as shown in FIG. 15 b.

FIGS. 15b to 15c illustrate a sampling plan being decomposed acrosssub-sampling plans of three wafers. The example of FIG. 15b does howevernot give the original spatial distribution, if all three sample plans onwafer level are stacked together. This will result in a worse estimationof the properties of the sampled lot.

Another choice that does allow for correct stacking is illustrated inFIG. 15c . However, if the distribution is done carelessly, as is donein the example of FIG. 15c , the sampling results per wafer may yieldunusable results again, because the estimation for some wafers may notbe very accurate.

FIGS. 16a and 16b illustrate a sampling plan being decomposed acrosssub-sampling plans of three wafers in a better way than illustrated inFIGS. 15b and 15c . The sub-sample plans are optimized per wafer, suchthat (1) the decomposed sampling schemes are useful, and (2) they can bestacked together to the original layout. For instance the schemeillustrated in FIG. 16a has a better cross-wafer spatial distribution,compared to that of FIG. 15c . This scheme has similar problems however,but at the cross-field level, and the estimation of the properties ofthe fields cannot be determined reliably. If this finer detail is alsotaken into account, one may end up with an optimal scheme as illustratedin FIG. 16 b.

FIG. 16c illustrates the exposure order for fields and a sub-samplingplan. The decomposition of the intrafield sampling plans is performedsuch that each three consecutive fields, in the exposure orderillustrated by the serpentine line 1602 in FIG. 16c , stacked togetherresult in a complete field.

The layouts illustrated in FIGS. 15c, 16a and 16b all are “complete”,that is, when the sub-sampling plans of all wafers are stacked there arenot “empty” spaces in the sample plan. Other embodiments may have thefull sample plan (here 12 fields of 9 marks) less dense so as to coveronly part of possible measurement sites on the wafer.

Another embodiment has an “incomplete” decomposed sampling plan. FIG. 17illustrates sampling plan being decomposed across sub-sampling plans ofsix wafers with some fields being not sampled. In this example, the lotsize is six wafers instead of three, and the sample plan can bedecomposed as shown in FIG. 17, where again the squares are exposurefields, the dots are sample points and the large circles represent thewafers. Some fields are skipped at some wafers, other fields are skippedat other wafers. When all sub-sampling plans are stacked together, thecomplete sample plan is achieved. This applies for all levels ofgranularity: not all fields need to be measured (as shown in FIG. 17),not all wafers need to be measured, and/or not all lots need to bemeasured.

Furthermore, if the number of wafers within one lot is not sufficient toallow this decomposition, multiple lots may be used. This would meanrunning two or more different static sampling plans in lot production.

Process control has been applied to the semiconductor industry for manyyears. Wafers are measured with metrology tools and a correction modelis applied to measured data in order to calculate model parameters.Those parameters are then used to control the process. Therefore, theperformance of process control depends on metrology measurement schemeand correction model. It is known that there is a trade-off betweenmetrology measurement effort and modeling accuracy.

Several optimality statistical criteria are used to optimize a metrologysampling scheme based on a given correction model. A popular optimalitycriterion is normalized model uncertainty (also called as G-optimality).The inference of normalized model uncertainty is shown below.

Least-square estimation: y=Cβ+∈

{circumflex over (β)}=(C^(T)C)⁻¹ C^(T)y

Assume y refers to measured data and

y ∈ R^(m × 1),m represents the number of measured points of a reduced sampling scheme;C represents a design matrix of a reduced sampling scheme, and C∈R^(m×n)refers to the number of fit coefficients, β indicates correctableparameters and β∈R^(n×1). cp refers to a design matrix of any measurableposition P and c_(p)∈R^(n×1). ε represents residual errors andε∈R^(m×1).

By assuming

$\beta = \begin{bmatrix}\beta_{0} \\\bullet \\\beta_{k}\end{bmatrix}$ and $C_{p} = \begin{bmatrix}1 \\\bullet \\x_{kp}\end{bmatrix}$

correctable errors at point P can be calculated as

y_(p) = β₀ + β₁x_(1p) + … + β_(k)x_(kp)y_(p)^(′) − E(y_(p)) = β₀^(′) − β₀ + (β₁^(′) − β₁)x_(1p) + … + (β_(k)^(′) − β_(k))x_(kp) = C_(p)^(T)(β^(′) − β)$\begin{matrix}{\sigma_{y_{p}^{\prime}}^{2} = {{E\left\lbrack \left( {y_{p}^{\prime} - {E\left( y_{p} \right)}} \right)^{2} \right\rbrack} = {{E\left\lbrack {{c_{p}^{T}\left( {\beta^{\prime} - \beta} \right)}\left( {\beta^{\prime} - \beta} \right)^{T}c_{p}} \right\rbrack}\because y}}} \\{= {{C\;\beta} + ɛ}} \\{= {c_{p}^{T}{E\left\lbrack {\left( {C^{T}C} \right)^{- 1}C^{T}{ɛɛ}^{T}{C\left( \left( {C^{T}C} \right)^{- 1} \right)}^{T}} \right\rbrack}c_{p}}} \\{= {\sigma_{noise}^{2}{c_{p}^{T}\left( {C^{T}C} \right)}^{- 1}c_{p}}}\end{matrix}$ where σ_(noise)² = E[ɛɛ^(T)].

Therefore,

σ_(y_(p)^(′)) = definition  of  model  uncertainty$\sigma_{noise}\sqrt{{c_{p}^{T}\left( {C^{T}C} \right)}^{- 1}c_{p}}$

The definition of normalized model uncertainty

$= {{\sigma_{y_{p}^{\prime}}/\sigma_{noise}} = \sqrt{{c_{p}^{T}\left( {C^{T}C} \right)}^{- 1}c_{p}}}$

As can be seen, the physical meaning of model uncertainty is standarddeviation of correctable errors for given position. By using a reducedsampling scheme and correction model, a design matrix can be built. Byassuming that the same variance at each position (σ_(noise) ²=E└εε^(T)┘,σ_(noise) is a constant), normalized model uncertainty can be calculatedper measurable (or specified) position. Following that, statisticalmeasures, e.g. maximum, mean plus 3 sigma . . . etc, can be used toevaluate a reduced sampling scheme. The optimal sampling scheme can thenbe determined.

A simple example is now given, with reference to FIG. 18, to explain theuse of metrology sampling scheme optimization (SSO). FIG. 18 is a graphof correctable errors, CE, in nm, versus metrology position, X, across awafer. The following are assumed:

(a) The full metrology layout is [−5, −4, −3, −2, −1, 0, 1, 2, 3, 4, 5],which is 11 positions in total, shown as black circles in FIG. 18.

(b) The fingerprint (or correctable errors) is shown in FIG. 18 as aparabolic fit curve 1802 and y=β₀+β₁x+β₂x², a given correction model.

(d) σ_(noise)=1 nm (uniform metrology measurement noise and processeffect over a wafer).

(c) There are no non-correctable errors (so-called NCE or residual).

In this case, the fingerprint calculated by measuring any 5 positionshas no difference from measuring full metrology layout with 11positions. In fact, measuring at least more than 2 positions issufficient and it doesn't matter at which positions the measurements areperformed.

With reference to FIG. 19, if real-world metrology noise (with anassumed normal distribution) is imposed to each position with 1nm-sigma, the fit curve 1902, even calculated from full layout, coulddeviate from the baseline fit curve 1802. The fit curve delta betweenthe curves 1802 and 1902 is actually the correctable delta. It can beexaggerated for a reduced sampling scheme. If [−1, 0, 1] were a reducedscheme, the fit curve could become upside-down, which would lead tosignificant large correctable delta.

Per position, normalized model uncertainty is equal to standarddeviation of correctable delta. Hence, normalized model uncertaintiesfor measuring full layout may be calculated as shown below.

In previous approaches using normalized model uncertainty (orG-optimality), it is assumed that every position has the same variances.However, in reality, the edge of a wafer suffers from more significantprocess effect than intermediate area of a wafer, and so does the centerof a wafer (where photo resist is deposited) and there sometimes existsunknown localized effects. These result in position-dependent variances.Besides, the deformation of overlay targets is not consistent over awafer either. So the metrology measurement noise shall be considered tobe position-dependent as well.

Because of non-uniform process effect/metrology noise over a wafer, theassumption made in previous approaches is no longer valid. An outputoptimal sampling scheme will be less robust in the real world.

In accordance with an embodiment, weighted least square (WLS) estimationis used to take position-dependent variances into account. The equationof model uncertainty is then re-inferred as shown below:

${{model}\mspace{14mu}{uncertainty}},{\sigma_{y_{p}^{\prime}} = \sqrt{{c_{p}^{T}\left( {C^{T}{WC}} \right)}^{- 1}c_{p}}},{where}$$W = \begin{bmatrix}{1/\sigma_{1}^{2}} & 0 & 0 \\\ldots & \ldots & \ldots \\0 & 0 & {1/\sigma_{k}^{2}}\end{bmatrix}$

where σ₁ ² represents the variance at position i of a reduced samplingscheme, k refers to the total number of measured positions of a reducedsampling scheme. This is referred to as weighted model uncertainty inorder to differentiate from normalized model uncertainty.

By using a reduced sampling scheme and correction model, a design matrixcan be built. By using a variance per sampling position, modeluncertainty can be calculated. The same statistical measures may be usedto evaluate the performance of a reduced sampling scheme. Hence, anoptimal sampling scheme can be determined.

FIG. 20 is a flowchart illustrating an embodiment with the sampling planupdated based on position-dependent variation of the property beingmeasured according to the sample plan.

The steps in this embodiment include:

2002—defining a sampling plan for measuring a property of a wafer.

2004—processing a wafer using the scanner;

2006—measuring the property of a substrate;

2008—determining the position-dependent variance the property and

2010—updating the sampling plan based on the position-dependent varianceof the measured property. The updating of the sampling plan may includemodifying the sampling across a wafer, for example by changing thesampling density and/or locations within the wafer, based for exampleupon the position-dependent variance of the measured property and using,for example, weighted least-square (WLS) estimation.

2012—measuring the property of a wafer using the updated sampling plan.

FIGS. 21 to 24 illustrate the effect of using weighted model uncertaintyrather than normalized model uncertainty with various simulated positiondependent variances.

Four different noise types are simulated and shown in FIG. 21. The waferedge variance is gradually increased from type to type.

Based on noise type 2102, which is not position-dependent, the optimalsampling scheme is at X positions across the wafer [−5, 0, 5]. Thisscheme can be applied to use cases with different variances at the edge,corresponding to noise types 2104, 2106 and 2108 illustrated in FIG. 20.These use cases are illustrated in FIGS. 22 to 24 in which biggermarkers refer to optimal sampling positions.

FIG. 22 is a graph of the weighted model uncertainty, in nm, for thenoise type with 10 nm wafer edge variance, corresponding to 2104 in FIG.21. As can be see in FIG. 22, when edge variance has been increased from5 nm to 10 nm, the optimal scheme still stands as [−5, 0, 5].

Once the edge variance is boosted to 12 nm, corresponding to 2106 inFIG. 21, as illustrated in FIG. 23, the sampling scheme [−4, 0, 4]starts to perform better than [−5, 0, 5].

The difference can be even increased to ˜1 nm if the edge variancereaches 18 nm, corresponding to 2108 in FIG. 21, as illustrated in FIG.24. Thus it can be seen that an optimal scheme may obtained usingposition-dependent variances instead of uniform variances.

The embodiment described with reference to FIGS. 14 to 17 provides anexample of operation of a method that can be implemented with aninspection apparatus. For example, with reference to FIGS. 4 and 25, aninspection apparatus may be configured for measuring a property of aplurality of substrates, the inspection apparatus comprising:

-   -   an illumination system, 2,12,13,15,16,17 in FIG. 4, configured        to illuminate a substrate with radiation;    -   a detection system, 18 and PU in FIG. 4, configured to detect        scattered radiation arising from the illumination; and    -   at least one processor, for example PU in FIG. 4, configured,        now with reference to FIG. 25, to:

2506—produce a sampling plan defined for measuring a property of asubstrate, wherein the sampling plan comprises a plurality ofsub-sampling plans. The sampling plan may be constrained to apredetermined fixed number of measurement points;

2508—control the inspection apparatus to perform a plurality ofmeasurements of the property of a plurality of substrates usingdifferent sub-sampling plans for respective substrates; and

2510—optionally, stack the results of the plurality of measurements toat least partially recompose the measurement results according to thesample plan.

The embodiment described with reference to reference to FIGS. 14 to 17may be combined, for example, with features of the embodiment describedwith reference to FIG. 11.

Such an example may be implemented in an inspection apparatus, such asmay be described with reference to FIGS. 4 and 26. The at least oneprocessor, for example PU in FIG. 4, may be configured, with referenceto FIG. 26, to:

2602—receive measured processing data related to processing of at leastone substrate using a processing apparatus;

2604—determine variation of the processing data; and

2606—produce the sampling plan based on the variation of the processingdata.

The steps 2508 and 2510 in FIG. 26 are the same as described withreference to FIG. 25.

The embodiment described with reference to reference to FIGS. 14 to 17may also be combined, for example, with features of the embodimentdescribed with reference to FIG. 12.

Such an example may be implemented in an inspection apparatus, such asmay be described with reference to FIGS. 4 and 27. The at least oneprocessor, for example PU in FIG. 4, may be configured, with referenceto FIG. 27, to:

2702—receive measured processing data related to processing of at leastone substrate using a processing apparatus, such as alignment data orlevelling data and receive measurements of a property of at least onesubstrate;

2704—determine a correlation of the measured processing data with themeasurements of the property; and

2706—produce the sampling plan based on the correlation of theprocessing data with the measured property.

The steps 2508 and 2510 in FIG. 27 are the same as described withreference to FIG. 25.

The embodiment described with reference to reference to FIGS. 14 to 17may also be combined, for example, with features of the embodimentdescribed with reference to FIGS. 9 and 20.

Such an example may be implemented in an inspection apparatus, such asmay be described with reference to FIGS. 4 and 28. The at least oneprocessor, for example PU in FIG. 4, may be configured, with referenceto FIG. 28, to:

2802—receive information on a characteristic affecting the substratesdifferently in two or more coordinates across a substrate. Theinformation may comprise process setup information, such as scannerprocess job information and/or scanner actuator information. Theinformation may comprise position-dependent variance across a substrateof the measured property; and

2806—produce the sampling plan configured to be different in two or morecoordinates across the substrate based on the received information onthe characteristic. When the information comprises position-dependentvariance across a substrate of the measured property, the at least oneprocessor may be configured to produce the sampling plan using weightedleast-squares estimation, as described with reference to FIG. 20.

The steps 2508 and 2510 in FIG. 28 are the same as described withreference to FIG. 25.

The embodiment described with reference to reference to FIGS. 14 to 17may also be combined, for example, with features of the embodimentdescribed with reference to FIGS. 9 and 20, including the updating ofthe sample plan.

Such an example may be implemented in an inspection apparatus, such asmay be described with reference to FIGS. 4 and 29. The at least oneprocessor, for example PU in FIG. 4, may be configured, with referenceto FIG. 29, to:

2900—control the inspection apparatus to perform a plurality ofmeasurements of the property of a plurality of substrates usingdifferent sub-sampling plans for respective substrates. This may beafter production of the sampling plan, in accordance with steps 2506 and2508 in FIG. 25.

2802—as described with reference to 2802 in FIG. 28, receive informationon a characteristic affecting the substrates differently in two or morecoordinates across a substrate. The information may comprise processsetup information, such as scanner process job information and/orscanner actuator information. The information may compriseposition-dependent variance across a substrate of the measured property;

2906—produce the sampling plan updated separately in two or morecoordinates across the substrate based on the received information on acharacteristic affecting the substrates differently in two or morecoordinates across a substrate. When the information comprisesposition-dependent variance across a substrate of the measured property,the at least one processor may be configured to produce the samplingplan using weighted least-squares estimation, as described withreference to FIG. 20; and

2908—control the inspection apparatus to perform a plurality ofmeasurements of the property of at least one substrate using differentupdated sub-sampling plans for the respective at least one substrate.

The step 2510 in FIG. 29 is the same as described with reference to FIG.25.

It is possible to separate between within wafer and wafer-to-wafermeasurements by distributing the sampling plan across more than onewafer using the sub-sampling plans and thus define two categories ofmeasurement points. The first category is for “within wafer” informationand the second category is for “between wafer” information. Furthermore,as has been described, sampling may be varied in two or more coordinates(for example x, y and/or radius). Both approaches achieve an optimallycontrolled lithographic apparatus on the basis of a given constraint ofa maximum number of say M measurements over a series of N exposed andmeasured wafers. The optimal control may be quantified using thestandard deviation of error of a property such as overlay or alignment.

The distribution can thus involve selection of a number of measurementpoints per wafer over a plurality of wafers and also the determinationof the location of the measurement points across the wafer.

For the distribution over a plurality of wafers: a number selection canbe made: n1 measurement points for the within wafer information and n2measurement points for between wafer information; next a locationdistribution for both n1 and n2 may be made (where n1+n2 is about M/N).For this sampling optimization the quality of the model (expressed inmodel uncertainty and non-correctable residuals) may be used as aboundary condition.

For the distribution across the wafer, a location distribution may beused which in density is different in x, y and/or radius to match fordifferences in these directions with respect to, for example:lithography or metrology equipment capabilities; chip design rules withdifferent constraints in x versus y direction; and wafer process effectswith radial or irregular variation patterns. These differences may beused as pre-information/boundary conditions for sampling optimization.

Embodiments can be used on a stand-alone metrology tool, but running onan integrated tool is also convenient because the cluster throughput ofa scanner with an integrated metrology tool may be used optimally.

The methods described herein can be implemented using the processingunit PU of an inspection apparatus. The processing unit can beintegrated in the scatterometer, as illustrated in FIGS. 3 and 4, or itmay be located elsewhere, for example as a stand-alone unit, ordistributed across apparatuses which may include the inspectionapparatus.

Embodiments also include computer program products containing one ormore sequences of machine-readable instructions for measuring a propertyof a substrate, the instructions being adapted to cause one or moreprocessors to perform a method or steps according to any of theembodiments described herein.

Although specific reference may be made in this text to the use oflithographic apparatus in the manufacture of ICs, it should beunderstood that the lithographic apparatus described herein may haveother applications, such as the manufacture of integrated opticalsystems, guidance and detection patterns for magnetic domain memories,flat-panel displays, liquid-crystal displays (LCDs), thin-film magneticheads, etc. The skilled artisan will appreciate that, in the context ofsuch alternative applications, any use of the terms “wafer” or “die”herein may be considered as synonymous with the more general terms“substrate” or “target portion”, respectively. The substrate referred toherein may be processed, before or after exposure, in for example atrack (a tool that typically applies a layer of resist to a substrateand develops the exposed resist), a metrology tool and/or an inspectiontool. Where applicable, the disclosure herein may be applied to such andother substrate processing tools. Further, the substrate may beprocessed more than once, for example in order to create a multi-layerIC, so that the term substrate used herein may also refer to a substratethat already contains multiple processed layers.

Although specific reference may have been made above to the use ofembodiments in the context of optical lithography, it will beappreciated that embodiments may be used in other applications, forexample imprint lithography, and where the context allows, is notlimited to optical lithography. In imprint lithography a topography in apatterning device defines the pattern created on a substrate. Thetopography of the patterning device may be pressed into a layer ofresist supplied to the substrate whereupon the resist is cured byapplying electromagnetic radiation, heat, pressure or a combinationthereof. The patterning device is moved out of the resist leaving apattern in it after the resist is cured.

The terms “radiation” and “beam” used herein encompass all types ofelectromagnetic radiation, including ultraviolet (UV) radiation (e.g.having a wavelength of or about 365, 355, 248, 193, 157 or 126 nm) andextreme ultra-violet (EUV) radiation (e.g. having a wavelength in therange of 5-20 nm), as well as particle beams, such as ion beams orelectron beams.

The term “lens”, where the context allows, may refer to any one orcombination of various types of optical components, includingrefractive, reflective, magnetic, electromagnetic and electrostaticoptical components.

While specific embodiments have been described above, it will beappreciated that the invention may be practiced otherwise than asdescribed. For example, the invention may take the form of a computerprogram containing one or more sequences of machine-readableinstructions describing a method as disclosed above, or a data storagemedium (e.g. semiconductor memory, magnetic or optical disk) having sucha computer program stored therein.

The descriptions above are intended to be illustrative, not limiting.Thus, it will be apparent to one skilled in the art that modificationsmay be made to the invention as described without departing from thescope of the claims set out below.

The invention claimed is:
 1. A method comprising: generating differentsub-sampling plans, each sub-sampling plan being for an inspectionapparatus to measure a property of a respective substrate of a pluralityof substrates, the inspection apparatus comprising an illuminationsource and a detector; and measuring, using the inspection apparatus,the property of each substrate of the plurality of substrates based on arespective sub-sampling plan of the different sub-sampling plans.
 2. Themethod of claim 1, further comprising stacking the measured property foreach substrate of the plurality of substrates to generate a measurementresult for the plurality of substrates.
 3. The method of claim 1,wherein the plurality of substrates comprises substrates in more thanone lot of substrates.
 4. The method of claim 1, wherein the generatingcomprises decomposing a sampling plan for the inspection apparatus tomeasure the property of the plurality of substrates into the differentsub-sampling plans.
 5. The method of claim 1, wherein each sub-samplingplan of the different sub-sampling plans is constrained to apredetermined fixed number of measurements.
 6. The method of claim 1,wherein each sub-sampling plan of the different sub-sampling plans isdistributed across a plurality of exposure fields of the respectivesubstrate of the plurality of substrates.
 7. The method of claim 1,further comprising: determining a variation of measured processing datarelated to processing at least one substrate of the plurality ofsubstrates, wherein the processing is performed by a lithographicapparatus; and wherein the generating is based on the variation of themeasured processing data.
 8. The method of claim 7, wherein theprocessing data comprises at least one of alignment data and levelingdata.
 9. The method of claim 1, further comprising: determining acorrelation between (a) a measured property of at least one substrate ofthe plurality of substrates and (b) measured processing data related toprocessing of at least one substrate of the plurality of substrates, theprocessing being performed by a lithographic apparatus; and wherein thegenerating is based on the correlation.
 10. The method of claim 1,wherein: the generating is based on a characteristic affecting theplurality of substrates differently in two or more coordinates across arespective substrate of the plurality of substrates; and eachsub-sampling plan of the different sub-sampling plans is different intwo or more coordinates across the respective substrate, and based onthe characteristic.
 11. The method of claim 10, further comprisingupdating the plurality of different sub-sampling plans separately in twoor more coordinates across the respective substrate based on thecharacteristic.
 12. The method of claim 10, wherein the characteristiccomprises process setup information.
 13. The method of claim 12, whereinthe process setup information comprises at least one of scanner processjob information and scanner actuator information.
 14. An inspectionapparatus comprising: an illumination source; a detector; and aprocessor configured to: generate different sub-sampling plans, eachsub-sampling plan configured for measuring a property of a respectivesubstrate of a plurality of substrates; control the inspection apparatusto measure the property of each substrate of the plurality of substratesbased on a respective sub-sampling plan of the different sub-samplingplans; and stack the measured property for each substrate of theplurality of substrates to generate a measurement result for theplurality of substrates, wherein the plurality of substrates comprisessubstrates in more than one lot of substrates.
 15. The inspectionapparatus of claim 14, wherein the different sub-sampling plans isdecomposed from a sampling plan for the inspection apparatus to measurethe property of the plurality of substrates.
 16. The inspectionapparatus of claim 14, wherein each sub-sampling plan of the differentsub-sampling plans is constrained to a predetermined fixed number ofmeasurements.
 17. The inspection apparatus of claim 14, wherein eachsub-sampling plan of the different sub-sampling plans is distributedacross a plurality of exposure fields of the respective substrate of theplurality of substrates.
 18. The inspection apparatus of claim 14,wherein: the processor is configured to generate the differentsub-sampling plans based on a variation of measured processing datarelated to processing at least one substrate of the plurality ofsubstrates; and the processing is performed by a lithographic apparatus.19. The inspection apparatus of claim 14, wherein: the processor isconfigured to generate the different sub-sampling plans based on acorrelation between (a) a measured property of at least one substrate ofthe plurality of substrates and (b) measured processing data related toprocessing of at least one substrate of the plurality of substrates; andthe processing is performed by a lithographic apparatus.
 20. Theinspection apparatus of claim 14, wherein the processor is configured togenerate the different sub-sampling plans based on a characteristicaffecting the plurality of substrates differently in two or morecoordinates across a respective substrate of the plurality ofsubstrates.
 21. The inspection apparatus of claim 20, wherein theprocessor is configured to update the different sub-sampling plansseparately in two or more coordinates across the respective substratebased on the characteristic.